Related papers: The centralizer of an element in an endomorphism r…
In this paper we study the diffeomorphism centralizer of a vector field: given a vector field it is the set of diffeomorphisms that commutes with the flow. Our main theorem states that for a $C^1$-generic diffeomorphism having at most…
We show that an idempotent lies in the center if it commutes with the other idempotents in the ring. Next, we introduce a partition of the set of idempotents and show that the automorphisms of the ring act transitively on each equivalence…
For a prime $p$, let $E_{p,p^m}=\{\begin{pmatrix}a&b\\p^{m-1}c&d\end{pmatrix}|a,b,c\in\mathbb{Z}_{p},~\mathrm{and}~d\in \mathbb{Z}_{p^{m}}\}$. We first establish a ring isomorphism from $\mathrm{End}(\mathbb{Z}_p\times\mathbb{Z}_p^m)$ onto…
In this paper, we mainly give characterizations of EP elements in terms of equations. In addition, a related notion named a central EP element is defined and investigated. Finally, we focus on characterizations of a generalized EP element,…
Let G be an isotropic reductive algebraic group over a commutative ring R. Assume that, for any maximal ideal M of R, the rank of the relative root system of G_{R_M} is greater or equal than 2. We show that under this assumption the…
Let $\mathbf G$ be a connected reductive algebraic group over an algebraically closed field, and let $s\in\mathbf G$ be a semisimple element. We show that the centraliser of $s$ is the semi-direct product of its identity component by its…
In [H. Duan and S. Liu, The isomorphism type of the centralizer of an element in a Lie group, Journal of algebra, 376(2013), 25-45], we have determined the isomorphism type of the centralizer of an element in a simpe Lie group. As a sequel…
We give a classification of $1$-primitive near-rings using sandwich centralizer near-rings
Let $f$ be a dominant endomorphism of the projective line, which is not conjugate to a power map $z\mapsto z^{\pm d}$. We consider the centralizers of the iterates of $f$,…
The centralizer of any non-scalar element of a free group algebra over a field is the coordinate ring of a nonsingular curve.
Let $R$ be a finite ring and let $\Cent(R)$ denote the set of all distinct centralizers of $R$. $R$ is called an $n$-centralizer ring if $|Cent(R)| = n$. In this paper, we characterize $n$-centralizer finite rings for $n \leq 7$.
In this note, we give a remark on the structure of centralizers of involutions in Coxeter groups.
Using the Geometrization Theorem we prove a result on centralizers in fundamental groups of 3-manifolds. This result had been obtained by Jaco and Shalen and by Johannson using different techniques.
This work is a review of results about centrally essential rings and semirings. A ring (resp., semiring) is said to be centrally essential if it is either commutative or satisfy the property that for any non-central element $a$, there exist…
In this paper, we study the centralizer of a partially hyperbolic diffeomorphism on $\mathbb{T}^3$ which is homotopic to an Anosov automorphism, and we show that either its centralizer is virtually trivial or such diffeomorphism is smoothly…
Let $F$ be a local non-archimedean field and $\mathcal{O}_F$ its ring of integers. Let $\Omega$ be a Bernstein component of the category of smooth representations of $GL_n(F)$, let $(J, \lambda)$ be a Bushnell-Kutzko $\Omega$-type, and let…
In this note, finite type epimorphisms of rings are characterized.
We relate the endomorphism rings of certain $D$-elliptic sheaves of finite characteristic to hereditary orders in central division algebras over function fields.
We show that the centralizer of a nonscalar element in the coproduct $k\langle X\rangle *k[Y]$ of a free associative algebra and a polynomial algebra over a given field is commutative. For $k\langle X \rangle$ this is part of Bergman's…
For an ample Hausdorff groupoid $G$, and the Steinberg algebra $A_R(G)$ with coefficients in the commutative ring $R$ with unit, we describe the centraliser of subalgebra $A_R(U)$ with $U$ an open closed invariant subset of unit space of…